I know that a rational number can always be expressed as a fraction, but can't we also say that it is a number that follows a definite pattern? Like one-third for example; it is never ending as a decimal, but it is predictable. This is observed in most if not all rational numbers, as far as I know.
So would it be possible for a number to be partially predictable?
Could a number have the exact same digits as pi, but instead have a periodic, predictable digit in it?
Is there a category of Rational irrational numbers (or irrational rational numbers)? For instance, could a number with digits like pi or the square root of 2 have rational parts?